Facing mounting pressure from local affiliates, which are reeling from sagging ratings, the Peacock Network will yank the funnyman from his coveted 10 p.m. time slot when NBC begins coverage of the Winter Olympics next month, sources told The Post yesterday.

The network also plans to cut Leno down from his current one hour to a half-hour, sources said.

That would give NBC the flexibility to air the newly slimmed down “Jay Leno Show” at either 11 or 11:30 p.m., depending on how talks go with the affiliates and Conan O’Brien, who follows Leno in NBC’s lineup.

Leno and O’Brien met with NBC bosses yesterday to discuss the situation, but no firm decisions have been made, the sources said.

Leno himself is either playing coy — or keeping his notoriously large chin up.

“It will give us time to do some traveling,” the funnyman riffed in last night’s monologue, acknowledging rumors he was being “canceled.”

“I understand that Fox is beautiful this time of year,” he added — demonstrating the caliber of humor behind his shriveling ratings.

As for the 10 p.m. slot, NBC may plug the hole with a mix of “Dateline” and “Law & Order–” or have affiliates run local news for an hour followed by Leno, O’Brien and Jimmy Fallon, with Carson Daly’s future less certain.

TMZ reported Conan will either be given the choice of the midnight to 1 a.m. time slot or leaving the network.

Leno’s show has averaged about 5.3 million total viewers, down 35 percent compared with NBC’s 10 p.m. hour last season.

The affiliates are eager to see anything more lucrative than Leno in that valuable time slot, particularly the evening newscast, on which they can make as much as 40 percent of their total revenue.

The network insists Leno is generating ratings in line with what NBC guaranteed advertisers, but the show has proven to be a poor lead-in for the affiliates’ local news at 11 p.m.

“Both Jay and the show are committed to working closely with them to find ways to improve the performance,” NBC said in a statement.

Local stations have become more vocal in their displeasure, especially after disappointing November sweeps.

“The affiliates have all been good soldiers and kept their mouths shut, but NBC cannot be promoting Leno during the Olympics,” said one station manager. “They have to have an announcement by the Olympics, or the affiliates will go nuts.”

Also fueling the rumors are reports NBC has put more pilots into production than in past years, possibly to find replacements at 10 p.m.